There are three lockers, each with two drawers. Each drawer contains one item - a pearl, or a clump of coal. In one locker both drawers contain pearls, in another both drawers contain clumps of coal, and in a the third locker one drawer contains a pearl, and the other contains a clump of coal.
You do not know which locker is which. You open one drawer and find a pearl. If you are allowed to open one more drawer, which one should you open to maximise your chances of finding another pearl?
Answer
You should open the other drawer in the same locker as the first drawer you opened.
To see why, look at it like this: If you open a drawer with a pearl in it, the probability that it is in the locker with two pearls is two in three, and one in three that it is in the locker with only one pearl. Since you are most likely in the two-pearl-locker, opening the other drawer in the same locker gives you the best chance of finding another pearl.